FRM Exam Part II · Derivatives

Credit Default Swap Pricing, TRS and Credit-Linked Notes

Updated 11 October 2026 · Fact-checked

A credit default swap (CDS) is protection against default on a reference entity. The buyer pays a periodic spread and receives (1 − recovery) × notional if default occurs. To price it, set the PV of premiums equal to the PV of expected protection payouts. Approximation: spread ≈ hazard rate × (1 − recovery).

Understand Credit Derivatives: CDS and Credit-Linked Products

A credit default swap transfers the credit risk of a reference entity from the protection buyer to the protection seller. The buyer pays a regular premium, quoted as a CDS spread in basis points a year on the notional. If a credit event occurs (such as bankruptcy or failure to pay), the seller pays the buyer the loss: notional × (1 − recovery rate). Settlement is physical (buyer delivers the defaulted bond for par) or cash (based on an auction-determined recovery price).

To price a CDS you need the hazard rate (also called default intensity). With a constant hazard rate λ, the probability of surviving to time t is e^(−λt). The default probability over one year is 1 − e^(−λ). In a reduced-form model, the spread is the premium that makes two legs equal in present value: the premium leg (spread payments made while the entity survives) and the protection leg (the loss payment if default occurs).

A useful shortcut is the credit triangle: spread ≈ λ × (1 − R), so λ ≈ spread ÷ (1 − R). Spreads reflect risk-neutral default probabilities. These are usually higher than real-world ones because they include a risk premium and liquidity effects.

Other products move credit risk differently. In a total return swap (TRS), the receiver gets all the asset's returns (coupons plus price change) and pays a funding rate such as SOFR plus a spread. So a TRS transfers market risk as well as credit risk. A CDS pays only on a credit event. A credit-linked note (CLN) is a funded note: the investor pays the principal up front and receives coupons, but loses principal if the reference entity defaults. It embeds a CDS in a bond and removes counterparty risk for the protection buyer, because the cash is already posted. The investor bears the reference entity's credit risk and also the issuer's credit risk.

The CDS basis is the CDS spread minus the bond's credit spread (often the asset-swap or Z-spread) for the same issuer. A negative basis means the bond's spread is wider than the CDS. A trader can buy the bond and buy CDS protection to earn the gap. The trade is funded, so the gain is the gap net of funding costs. A positive basis means the CDS is wider than the bond spread.

The factors differ in direction. Factors that push the basis positive include the cheapest-to-deliver option, strong demand for protection, and bond funding costs above the benchmark rate (such as SOFR). Factors that push it negative include counterparty risk on the protection seller and bond illiquidity.

Key formulas to remember

Credit triangle: CDS spread ≈ λ × (1 − R); λ is the annual hazard rate and R the recovery rate. It is an approximation that is good for flat curves.
Hazard rate from spread: λ ≈ s ÷ (1 − R); Use s in decimals, e.g. 120 bp = 0.0120.
Survival probability (constant hazard): Q(t) = e^(−λt); The cumulative default probability is 1 − e^(−λt).
Protection leg payout: Notional × (1 − R); Paid by the protection seller on a credit event.
Fair CDS spread: s = PV(protection leg) ÷ risky annuity (PV of 1 per year paid while the entity survives); Premium accrued up to the default date adds a small correction.
CDS basis: Basis = CDS spread − bond spread; A negative basis means that the bond spread is above the CDS spread.
Value of an existing CDS to the buyer: (Current market spread − contract spread) × risky annuity × notional; It is positive for the buyer if spreads have widened.

How to solve Credit Derivatives: CDS and Credit-Linked Products questions

Use this order for any CDS or credit derivative question.

1Identify the product: CDS, TRS, CLN, or index. Note who is the protection buyer or seller, and which party bears which risk.
2List the inputs: spread, recovery rate, hazard rate, maturity, notional, payment frequency.
3Convert units. Basis points to decimals (100 bp = 0.01). Check whether the spread is annual and whether the hazard rate is annual.
4Choose the method: the credit triangle for a quick estimate, or the PV-of-legs equation for an exact answer.
5Calculate: the hazard rate or default probability first, then the spread or payout. Use e^(−λt) for survival.
6For mark-to-market, use the spread change times the risky annuity times notional. Give the sign from the buyer's view.
7Check the interpretation: does the spread level make sense, and is the risk-neutral vs real-world distinction relevant?
8Match your answer to exactly one option. Watch for options built from common slips such as forgetting (1 − R).

Quickest way: Credit triangle shortcut

When to use it: Use it when a question gives a spread and recovery rate and asks for hazard rate or default probability, or the reverse, and says approximate or gives a flat curve.

Write s ÷ (1 − R) = λ.
Convert s to a decimal first.
For a one-year default probability, use λ directly or 1 − e^(−λ). The two are close when λ is small.
For a multi-year probability, use 1 − e^(−λt).
If the options are close, compute the exponential version.

Common mistakes in Credit Derivatives: CDS and Credit-Linked Products

Using the spread as the default probability.
Both are small percentages, so they look alike.
Fix: Divide the spread by (1 − R) to get the hazard rate. With R = 40%, the hazard rate is 1.67 times the spread.
Confusing a TRS with a CDS.
Both are described as credit derivatives.
Fix: A TRS passes on all return, including market price moves, with no credit event needed. A CDS pays only on a credit event.
Treating a CLN as unfunded.
It is linked to a CDS in structure.
Fix: A CLN is funded: the investor pays the principal up front. So the protection buyer (the issuer) has no counterparty risk, because the cash is already posted. The investor bears both the reference entity's credit risk and the issuer's credit risk.
Getting the sign of the basis wrong.
Students mix up which spread is subtracted.
Fix: Basis = CDS − bond spread. Bond spread of 150 bp and CDS of 120 bp gives −30 bp, a negative basis.
Treating CDS-implied default probabilities as real-world ones.
The formula looks like a plain probability calculation.
Fix: They are risk-neutral. They usually overstate real-world default frequency because they include a risk premium.
Forgetting that the payout is notional × (1 − R).
Students pay full notional.
Fix: Under physical settlement the buyer delivers the bond at par, so the net loss is still (1 − R) of notional.

Worked examples

Example 1

A five-year CDS on a company trades at 180 bp. The assumed recovery rate is 40%. Using the credit triangle, estimate the annual hazard rate and the probability of default within three years, assuming a constant hazard rate.

Show the solution

Convert the spread: 180 bp = 0.0180.
λ = 0.0180 ÷ (1 − 0.40) = 0.0180 ÷ 0.60 = 0.03, or 3% a year.
Three-year survival probability = e^(−0.03 × 3) = e^(−0.09).
e^(−0.09) ≈ 0.9139.
Default probability = 1 − 0.9139 = 0.0861.

Answer: The hazard rate is 3% a year. The three-year default probability is about 8.6%.

Example 2

A bank bought protection on a ₹50,00,00,000 notional five-year CDS at a contract spread of 100 bp. The market spread for the same CDS is now 140 bp. The risky annuity (PV of 1 per year paid while the entity survives) is 4.2. What is the approximate mark-to-market value to the protection buyer?

Show the solution

Spread change = 140 − 100 = 40 bp = 0.0040.
Value per unit notional = 0.0040 × 4.2 = 0.0168.
Multiply by notional: 0.0168 × ₹50,00,00,000 = ₹84,00,000.
The market spread rose, so protection is worth more than the buyer pays. The value is positive for the buyer.

Answer: The buyer has a gain of about ₹84,00,000.

Exam tips

Know the credit triangle cold. Many hazard-rate and default-probability questions reduce to it.
Questions often hide the trap in a single word: funded vs unfunded, buyer vs seller, or CDS spread vs bond spread.
For TRS questions, look for who bears price risk. The receiver bears the asset's price risk; the payer transfers the economic exposure but remains exposed to the receiver's default.
When a question mentions negative basis, think of arbitrage limited by funding costs, with bond illiquidity and counterparty risk on the protection seller as reasons it persists. For a positive basis, think of the cheapest-to-deliver option and strong demand for protection.
Always state the sign of a mark-to-market from the buyer's side.

Practice questions from Derivatives

Credit Derivatives: CDS and Credit-Linked Products in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.